A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{2}\]
Correct Answer: B
Solution :
\[\vec{a}-\vec{b}\] is unit vector, if \[|\vec{a}-\vec{b}|=1\] \[\Rightarrow \] \[|\vec{a}-\vec{b}{{|}^{2}}=1\] \[\Rightarrow \] \[|\vec{a}{{|}^{2}}-2\,\vec{a}.\vec{b}+|\vec{b}{{|}^{2}}=1\] \[\Rightarrow \] \[1-2|\vec{a}|\,\vec{b}|\,\cos \theta +1=1\Rightarrow 1=2\cos \theta \] \[\Rightarrow \] \[\cos \,\,\theta =\frac{1}{2}\Rightarrow \theta =\frac{\pi }{3}\]
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